In June, Trump and Kim opened up dialogue on denuclearization of the Korean peninsula after months of trading military threats and pointed barbs.
Moon and Kim, accompanied by their wives, visited Mount Paektu on the Chinese border.
Tuesday's meeting between the South's President Moon Jae-in and the North's leader Kim Jong Un is their third so far this year.
The nuclear-armed North invaded its neighbour in 1950, starting the Korean War.
South Koreans and the world have long viewed him with a mixture of ridicule and fear, becoming used to the sight of him presiding over missile launches...
"It is only the beginning," Moon told a press conference. "Yesterday was the first step and I think we had a good start."
Moon Jae-In favours engagement and dialogue with Pyongyang over its atomic and missile ambitions.
Hong Joon-Pyo, of Park's Liberty Korea party, who languished in third place in the 13-strong field on 16 percent, urged voters to support him, branding...
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